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SNP leader Nicola Sturgeon has said her party has been the most consistent anti-Brexit voice during the European election campaign.
Labour’s Scottish leader Lesley Laird said a new vote on Brexit was becoming more likely.
Conservative MP Colin Clark said next month’s Brexit bill will be “different” from what has gone before.
Liberal Democrat leader Vince Cable said his party could support it, if the public were given the final say.
UK voters take part in elections to the European parliament on Thursday.
Ms Sturgeon told the Andrew Marr show on BBC One that putting the Brexit issue back to people in a second vote would be the right way forward.
She added: “There is nobody I think in Scotland or across the UK that could doubt that the SNP is unequivocally and unambiguously anti-Brexit.
“Scotland’s not for Brexit. Scotland is for Europe and people in Scotland have an opportunity by voting SNP on Thursday to send that message very loudly and very clearly.”
Lesley Laird told Gordon Brewer that a new referendum is possible
Speaking later on Sunday Politics Scotland, Ms Laird said a new referendum on Brexit was becoming more likely, but not certain.
“That is absolutely now the direction that we see this ending up,” she said. “You cannot yet say.”
“We’re going to have these indicative votes. We don’t know what Theresa May will bring forward and we don’t know therefore what that final deal will look like.”
Colin Clark believes the prime minister will bring new ideas on Brexit before MPs
Mr Clark told the programme that the Brexit proposition being brought to the Commons was not simply a re-run of the measure which had previously been rejected by MPs.
He said: “The bill will be different when it comes back. It has to be different when it comes back and has to bring more of the party together.
“And I believe if Labour were given a free vote, the bill would pass.”
Vince Cable believes the voters should have the final say
Mr Cable said the Liberal Democrats could back the prime minister, but only if the public were given the final say on the terms of exit in a referendum.
He said his party had discussed the “practicalities” of holding another public vote and it was possible before the 31 October deadline.
“We need a proper referendum that will come to a resolution on the issue, with remain on the ballot paper.”
Patrick Harvie thinks the European vote should be about more than Brexit
Patrick Harvie of the Scottish Greens said voters on Thursday should not simply look at a party’s stance on Brexit.
“Electing a Green MEP for Scotland will electing someone who’ll stand up not just for Scotland’s place in Europe,” he said, “but also for the issues like the climate emergency and tackling the refugee crisis in a humane and decent manner.”
The Brexit Party the issue of making Brexit happen comes before everything else.
Their representative Louis Stedman-Bryce added: “The message really is that we have to focus on democracy before we can focus on anything else.
“We have to make Brexit happen.”
Louis Stedman-Bryce of the Brexit Party wants leaving the EU to be an overriding priority
